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From Memory Alpha, the free Star Trek reference
Are you challenging me to a duel, Captain Kirk?! - Trelane, the Retired General of Gothos TOS: "The Squire of Gothos"
A duel was a sporting event where two or more opponents engage in combat against each other; the victor was often the one who was unscathed or generally in a better position than the opponent at the end of the event.
James Kirk and Trelane, the Squire of Gothos battled each other in a duel of guns. Later, they used swords. (TOS: "The Squire of Gothos")
In the 24th century, Frenchmen, like Jean-Luc Picard, used fencing to duel. He invited Guinan to participate in a duel, and she promptly defeated Picard using a fake wounded tactic. (TNG: "I Borg")